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On the Markus-Yamabe Conjecture

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Automorphisms of Affine Spaces

Abstract

The so called Global Asymptotic Stability Jacobian Conjecture or Markus — Yamabe Conjecture (MYC(n)) is as follows:

If f ∈ C 1(ℝn, ℝn) satisfies the so called Markus — Yamabe Condition, i.e. for all x ∈ ℝn all eigenvalues of D f (x) have a negative real part and if f(0) = 0, then 0 is a global attractor of the ODE

$$\dot{x} = f\left( x \right).$$
(1)

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Authors and Affiliations

  1. Mathematisches Institut, Universität Basel, Rheinsprung 21, CH-4051, Basel, Switzerland

    Robert Feßler

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  1. Robert Feßler
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Editors and Affiliations

  1. Department of Mathematics, Catholic University of Nijmegen, 6525 ED, Nijmegen, The Netherlands

    Arno van den Essen

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© 1995 Springer Science+Business Media Dordrecht

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Feßler, R. (1995). On the Markus-Yamabe Conjecture. In: van den Essen, A. (eds) Automorphisms of Affine Spaces. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8555-2_7

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  • DOI: https://doi.org/10.1007/978-94-015-8555-2_7

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4566-9

  • Online ISBN: 978-94-015-8555-2

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